Generalized commutative quaternions of the Fibonacci type
نویسندگان
چکیده
Abstract Quaternions are a four-dimensional hypercomplex number system discovered by Hamilton in 1843 and next intensively applied mathematics, modern physics, computer graphics other fields. After the discovery of quaternions, modified quaternions were also defined such way that commutative property multiplication is possible. That called as studied used for example signal processing. In this paper we define generalized based on them explore Fibonacci type quaternions.
منابع مشابه
Fibonacci Sequences of Quaternions
In this paper Fibonacci sequences of quaternions are introduced, generalizing Fibonacci sequences over commutative rings, and properties of such sequences are investigated. In particular we are concerned with two kinds of Fibonacci sequences of generalized quaternions over finite fields Fp, with p an odd prime, and their periods.
متن کاملGeneralized Quaternions
The quaternion group Q8 is one of the two non-abelian groups of size 8 (up to isomorphism). The other one, D4, can be constructed as a semi-direct product: D4 ∼= Aff(Z/(4)) ∼= Z/(4) o (Z/(4))× ∼= Z/(4) o Z/(2), where the elements of Z/(2) act on Z/(4) as the identity and negation. While Q8 is not a semi-direct product, it can be constructed as the quotient group of a semi-direct product. We wil...
متن کاملthe investigation of the relationship between type a and type b personalities and quality of translation
چکیده ندارد.
Binomial Identities Involving The Generalized Fibonacci Type Polynomials
We present some binomial identities for sums of the bivariate Fi-bonacci polynomials and for weighted sums of the usual Fibonacci polynomials with indices in arithmetic progression.
متن کاملRoots of a Type of Generalized Quasi-Fibonacci Polynomials
Let a be a nonnegative real number and define a quasi-Fibonacci polynomial sequence by F a 1 (x) = −a, F a 2 (x) = x − a, and F a n (x) = F a n−1(x) + xF a n−2(x) for n ≥ 2. Let ra n denote the maximum real root of F a n . We prove for certain values of a that the sequence {ra 2n} converges monotonically to βa = a 2 + a from above and the sequence {ra 2n+1} converges monotonically to βa from be...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Boletin De La Sociedad Matematica Mexicana
سال: 2021
ISSN: ['2296-4495', '1405-213X']
DOI: https://doi.org/10.1007/s40590-021-00386-4